is a late 2009 imac able to update safari browser

pretty straight forward question... many websites nop longer are working with half stating that my browser will no longer work jan 1, and I need to update browser but I cannot find an update available through system preferences and I do not see a system services. when I look in about this Mac I hit updates and th3re is no safari browser update available... so Imo asking if my iMac is to old for an update or??